Dominance relationships are a defining feature of the social organization of many animal species. Populations structured by absolute dominance usually maintain a generally linear hierarchy, while relative dominance occurs, for example, within territorial populations where an animal is likely to be dominant within its territory. Because relative dominance is dependent on social context, the traits associated with it are often unclear. Green anole lizards, Anolis carolinensis, are an ideal system in which to determine dominance-related traits, as anoles use territorial defence in most natural environments, but establish a dominance hierarchy at high densities such as those that occur in captivity. We hypothesized that anoles use similar morphological and behavioural traits to determine social status under both forms of social organization. To test this, we studied a natural population of anoles to determine the traits most predictive of male territory size and quality (as measured by the number of females overlapping a male's territory). While these measures of territory may be related, they measure different components of territorial success. We then used mathematical ranking algorithms to quantify dominance in a tournament of paired arena trials, and identified traits associated with rank. Our results showed that lizards with wider heads had higher social rank, while those with longer heads were more successful at territorial defence. We also found that, independently of morphology, lizards who behaved more aggressively ranked higher in dominance trials, although behaviour did not predict measures of territory. Together, our results indicate that different traits may determine absolute and relative dominance in the green anole.